PUB - Publikationen an der Universität Bielefeld

We develop a suitable version of the stable module category of a finite groupG over an arbitrary commutative ring k. The purpose of the construction is toproduce a compactly generated triangulated category whose compact objects arethe finitely presented kG-modules. The main idea is to form a localisation ofthe usual version of the stable module category with respect to the filteredcolimits of weakly injective modules. There is also an analogous version of thehomotopy category of weakly injective kG-modules and a recollement relating thestable category, the homotopy category, and the derived category of kG-modules.